Group Delay Based Averaging

ABSTRACT

Embodiments of the present invention provide techniques and methods for improving signal-to-noise ratio (SNR) when averaging two or more data signals by finding a group delay between the signals and using it to calculate an averaged result. In one embodiment, a direct average of the signals is computed and phases are found for the direct average and each of the data signals. Phase differences are found between each signal and the direct average. The phase differences are then used to compensate the signals. Averaging the compensated signals provides a more accurate result than conventional averaging techniques. The disclosed techniques can be used for improving instrument accuracy while minimizing effects such as higher-frequency attenuation. For example, in one embodiment, the disclosed techniques may enable a real-time oscilloscope to take more accurate S parameter measurements.

FIELD OF THE INVENTION

The present invention relates to improved methods for averaging datasignals while minimizing distortion caused by effects such as jitter.

BACKGROUND OF THE INVENTION

Direct averaging is often used to improve measurement accuracy inmeasurement instruments, such as oscilloscopes. By taking the average ofmultiple signals (or averaging multiple samples acquired from a singlesignal), the signal-to-noise ratio (SNR) of the result can be increased,since non-repeating noise and distortion are averaged out. But, when thesignals have jitter, the averaged result may be distorted. When thesignals are averaged, this jitter causes higher-frequency portions ofthe result to be attenuated more than the rest of the result. This cantypically be seen as slower rising edges in the averaged result.

Often, measurement instruments may introduce jitter into the signalsthat they are measuring. For example, trigger jitter in real-timeoscilloscopes introduces jitter into samples acquired by the scope.Thus, these instruments may not be able to make measurements asaccurately as more expensive devices, even when averaging is used. Thus,there is a need for improved averaging techniques to minimize the effectthat jitter has on the averaged result.

Improved averaging techniques could be useful for a number of differentsignal processing applications, and might allow instruments withacquisition jitter to replace more expensive instruments. For example,in one embodiment, improved averaging techniques could allow real-timeoscilloscopes to measure S-parameters of a device under test.

In one example, the disclosed techniques might allow a real-timeoscilloscope to measure S-parameters without needing additionalinstruments such as a vector network analyzer (VNA). As bit ratesincrease, high speed serial data link simulation and measurementsincreasingly need to use S parameters when modeling components in thedata link. For example, to fully characterize and simulate the serialdata link 100 shown in FIG. 1, the output impedance (represented byreflection coefficient S₂₂) of the transmitter (Tx) 105, input impedance(represented by reflection coefficient S₁₁) of the receiver (Rx) 115,and the full S parameters (S₁₁, S₁₂, S₂₁, and S₂₂) of the channel 110are all needed.

Traditionally, a vector network analyzer (VNA) or a time-domainreflectometry (TDR) system with a sampling oscilloscope is needed tomeasure these types of S parameters for two-port or multi-port networkcharacterization. These specialized instruments are often expensive, andare not widely available. In contrast, real-time oscilloscopes arecommonly used to debug, test, and measure high speed serial data links.It would be convenient to use real-time oscilloscopes to measure the Sparameters of a data link.

Unfortunately, while some previous methods allow a real-timeoscilloscope to measure S parameters or related functions, they do notenable the scope to take accurate enough measurements to eliminate theneed for additional VNA or sampling oscilloscope-based TDR solutions.For example, one prior art solution by Agilent (described in U.S. patentapplication Ser. No. 13/247,568 (“the '568 application”)) uses precisionprobes to measure probe impedance and transfer functions for a DeviceUnder Test (DUT). These measurements may then be used to create embed ordeembed filters to compensate for the measured system characteristics.But the transfer functions measured using this method do not provideaccurate delay information for the DUT. For example, a longer highquality cable may have the same magnitude loss as a shorter butlower-quality cable. But these two cables have very different groupdelay characteristics. Because the method disclosed in the '568application does not measure accurate delay information, it is notaccurate enough to determine which type of cable is being used.

U.S. patent application Ser. No. 14/673,747 (“the '747 application”)does describe a method of measuring full S parameters using a real-timescope, along with a signal generator and a power divider. But the methoddisclosed in the '747 application is still prone to measurement errorsdue to trigger jitter that is inherent in real-time scopes.

As discussed above, accuracy of real-time scopes can be improved byusing averaging. But real-time scopes have trigger jitter, which causesthe higher-frequency portions of the signal to be attenuated more thanthe rest of the signal. This can typically be seen as slower risingedges in the measured signal. Because prior art averaging solutions donot address this attenuation, they do not enable real time oscilloscopesto make measurements as accurately as other instruments such as VNAs orsampling scopes.

In addition, when a repeating data pattern is averaged, the patternsmust all be aligned. Traditionally, the patterns are aligned based onedge crossings, or by using cross-correlation. But noise in the patternscan distort the edge crossings, causing a loss of accuracy in edge-basedmethods. And cross-correlation is computationally expensive.

Thus, there is a need for improved averaging techniques to take moreaccurate signal measurements.

SUMMARY OF THE INVENTION

Embodiments of the present invention use group delay to improve thesignal-to-noise ratio when averaging multiple signals. This eliminatesthe distortion that occurs in conventional averaging techniques due tojitter. The disclosed techniques may be used in any application thatuses averaging, or by any type of device or instrument. For example, inone embodiment, the disclosed techniques may be used by a real-timeoscilloscope to measure S parameters with greater accuracy, despite thescope's inherent trigger jitter. This may allow the real-timeoscilloscope to replace more expensive devices. In another embodiment,the disclosed techniques may be used when averaging repetitive datapatterns that have been obtained from multiple acquisitions, or whenaveraging multiple portions of repeating data signals that have beenobtained from a single long acquisition. And, because the disclosedtechniques are computationally efficient, they may be used by devicesthat have less processing power.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a prior art high speed serial data link system.

FIG. 2 depicts the phase and magnitude for the average of two vectors.

FIG. 3 depicts a method for compensating time shifts between datasignals in accordance with one embodiment of the present invention.

FIG. 4 depicts a magnitude plot obtained in accordance with thedisclosed invention, compared with a magnitude plot obtained using priorart averaging techniques.

FIG. 5 depicts insertion loss measured in accordance with the disclosedinvention, compared to insertion loss measured with a prior art VNA.

FIG. 6 depicts an exemplary instrument for performing clock recovery inaccordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 depicts a high-level block diagram of a serial data link system.Transmitter (Tx) 105 is connected to a receiver (Rx) 115 through achannel 110. As is known in the art, the channel 110 may consist of anyphysical transmission medium, including copper wire, coaxial cable,optical fiber, or (in the case of wireless transmission) the air. Achannel 110 may also consist of multiple mediums.

Real-time oscilloscopes are commonly used to measure characteristics ofserial data link systems. As discussed above, the trigger jitter in realtime scopes introduces horizontal shifts which cause thehigher-frequency portions of the measured signal to be attenuated whenaveraging is used. The horizontal time shift (also called jitter)between two otherwise identical data signals (e.g., signals a and b)causes a constant group delay between the two signals. This group delaycauses a proportional phase difference ΔΦ between the two signals. Therelationship between time difference At and phase difference ΔΦ can beseen in the following equation:

ΔΦ(f)=2π*f*Δt   (eq 1)

The impact that these horizontal shifts have on the averaged result canbe examined in the frequency domain. At a particular frequency f, eachsignal may be represented by a vector in complex coordinates, as shownin FIG. 2. In FIG. 2, two data signals a and b are represented by thevectors {right arrow over (a)} 205 and {right arrow over (b)} 210. Thephase difference between {right arrow over (a)} 205 and {right arrowover (b)} 210 is ΔΦ 220.

Taking the direct average of {right arrow over (a)} 205 and {right arrowover (b)} 210 yields vector {right arrow over (c)} 215. As depicted inFIG. 2, vector {right arrow over (c)} 215 points to the mid-point ofline {right arrow over (ab)} 225. The vector {right arrow over (c)} 215is perpendicular to the line {right arrow over (ab)} 225, and bisectsthe angle ΔΦ. The magnitude of {right arrow over (c)} 215 is cos(ΔΦ/2)times the common magnitude of {right arrow over (a)} 205 and {rightarrow over (b)} 210. When {right arrow over (a)} 205 and {right arrowover (b)} 210 are not in phase (i.e., when ΔΦ 220 is not zero), themagnitude of {right arrow over (c)} 215 will be less than the commonmagnitude of {right arrow over (a)} 205 and {right arrow over (b)} 210.

The disclosed techniques address the time shift between data signals byexplicitly measuring and compensating Δt before performing theaveraging. By compensating the time shifts, the phase difference ΔΦ 220is reduced to zero for all data signals that need to be averaged. So theaveraged vector {right arrow over (c)} 215 will have the same magnitudeas {right arrow over (a)} 205 and {right arrow over (b)} 210, sincecos(0)=1.

According to one embodiment of the present invention, two or more datasignals (x₁, . . . , x_(n)) are acquired and a direct average of all ofthe data signals x is computed. Group delays (y₁, . . . , y_(n)) arecomputed for each individual signal (x₁, . . . , x_(n)) and an averagegroup delay y is computed for the average signal x. Next, the differencebetween each signal's group delay (y₁, . . . , y_(n)) and the averagegroup delay y is computed. The differences are compensated to createcompensated signals (z₁, . . . , z_(n)). Finally, the compensatedsignals are averaged together to create an averaged result z.

FIG. 3 depicts an exemplary flowchart for performing group delay-basedaveraging according to one embodiment of the present invention. At step300, two or more data signals (x₁, . . . , x_(n)) are acquired. A directaverage of all of the data signals is computed at step 305, to obtain anaveraged signal x.

In the embodiment shown in FIG. 3, the group delays are determined usingby using phases of each signal. At step 310, the phase Φ(f) of theaveraged signal x is determined. In one embodiment, the phase iscomputed by performing a Fast-Fourier Transform (FFT) for the averagedsignal x. In another embodiment, the phase Φ(f) is computed by taking aderivative of the averaged signal x, and performing an FFT for thederivative of x. In both embodiments, a windowing function mayoptionally be applied before performing the FFT. The windowing functionimproves performance by eliminating leakage into adjacent frequencybins.

At step 315, phases Φ(f)_(i) are computed for the individual datasignals similar to step 310. In one embodiment, phases Φ(f)_(i) arecomputed by performing an FFT for each signal (x₁, . . . , x_(n)). Inembodiments where the derivative was used to determine x in step 310,the derivative of each signal must be computed at step 315 beforeperforming an FFT to find the phase of each derivative. In bothembodiments, a windowing function may optionally be applied beforeperforming the FFTs.

In steps 310 and 315, the decision to perform an FFT on the signal orits derivative may depend on what type of data the signal contains. Forexample, when the starting and ending values of the signal are not closeto each other (e.g., as in a step-like waveform), it may be preferableto use the signal's derivative. For other types of signals, using thesignal itself may yield better results.

At step 320, a phase difference ΔΦ(f)_(i) between each individual phaseΦ(f)_(i) and the average phase Φ is computed. In one embodiment, thephases found in steps 310 and 315 may be unwrapped and used to computethe phase difference for each individual signal. For example, theunwrapped average phase Φ(f) may be subtracted from the unwrappedindividual phases Φ(f)_(i) to obtain phase differences (ΔΦ(f)_(i), . . ., ΔΦ(f)_(n)). Any other suitable method of computing phase differencesmay also be used.

At step 325, the slope ΔΦ_(i)(f) of each phase difference ΔΦ(f)_(i) iscomputed. In one embodiment, a straight line fit may be performed usingthe Least Mean Squared (LMS) method. A weighting function may beoptionally used when performing the LMS fit. For example, this phaseplot is smoother at lower frequencies than it is at higher frequencies.To obtain a more accurate slope, it may be useful to weight the lowfrequency values more than the high frequency values.

The phase slopes may be compensated directly, or converted to timedifferences first. In embodiments where time differences arecompensated, the slopes ΔΦ_(i)(f) are first used to determine a timeshift Δt_(i) for each signal x₁ . . . x_(n) at step 330. For example, eq1 above describes a relationship between slope and time shift. In oneembodiment, the time shift Δt_(i) for each signal may be determined bydividing the slope of that signal's phase difference by 2π*f (where f isthe frequency). In other words:

$\begin{matrix}{{\Delta \; t_{i}} = \frac{\Delta \; {\Phi_{i}(f)}}{2\; \pi*f}} & \left( {{eq}\mspace{14mu} 2} \right)\end{matrix}$

At step 335, the signals are compensated. In embodiments where timeshifts were computed at step 330, the time shifts Δt₁ . . . Δt_(n) arecompensated. In one embodiment, the result of the FFT that was performedon each individual signal (or its derivative) x_(i), . . . , x_(n) maybe multiplied by exp(j*2π*f*Δt_(i)) to obtain compensated FFT resultsz_(i), . . . , z_(n) -where j represents the square root of negativeone, f is frequency, and Δt_(i) is the time shift of each signal. Inother embodiments, the compensated FFT results z_(i), . . . , z_(n) maybe obtained by multiplying the FFT results by exp(j*ΔΦ_(i)(f)) instead.

At step 340, the compensated FFT results z_(i), . . . , z_(n) areaveraged and converted to the time domain, in order to obtain anaveraged time-domain result. In one embodiment, the compensated signalsz_(i), . . . , z_(n) are averaged to obtain an averaged result z, and aninverse FFT (IFFT) is used to convert the averaged result z to the timedomain. In another embodiment, an IFFT may be performed to convert eachcompensated signal z_(i), . . . , z_(n) to the time domain first, beforeaveraging the results of the IFFTs to obtain an averaged time-domainresults z.

In embodiments where the signals' derivatives were used in step 310 or315, the averaged result obtained in step 335 is integrated at step 345to return the averaged result to its correct form. Although theembodiment depicted in FIG. 3 uses phase and time derivatives, any knownmethods for determining and compensating group delays may be usedinstead.

The disclosed group delay based approach has several advantages. First,by compensating for time shifts, the disclosed technique improvesoverall SNR by preserving the averaged signal level at higherfrequencies. Second, the disclosed techniques use FFT and IFFT, whichare more computationally efficient than conventional approaches (such ascross-correlation methods) that must align the data signals beforeaveraging them. Third, the disclosed techniques obtain an averagedresult by using a Least Mean Squared (LMS) type of line fit, whichresults in a single value that can be used directly to compensate thetime shifts. In comparison, conventional cross correlation methodsrequire an extra interpolation step to find the value of the time shiftsΔt_(i). Fourth, the disclosed techniques use all of the data points ineach data signal to obtain the value of Δt_(i). In contrast,conventional methods based on edge-crossing only use a few data pointsaround the edges of the waveform in each data signal. Finally, thedisclosed techniques may be used to provide a computationally efficientmanner of averaging a repeating data pattern, while providing moreaccurate results than traditional edge-based methods.

FIG. 4 depicts magnitude plots for a step like data signal that has gonethrough a derivative operation. As shown in FIG. 4, the magnitude of agroup-delay based average result that was obtained in accordance withthe present invention (shown by plot 405) is improved by about 2 dB at30 GHz when compared to a conventionally-averaged result (shown by plot410).

FIG. 5 depicts an insertion loss measurement result 505 obtained using areal-time oscilloscope in accordance with the present invention. Asshown in FIG. 5, the insertion loss curve 505 correlates with aninsertion loss measurement 510 that was taken with a VNA, forfrequencies up to 25 GHz. This illustrates that the disclosed techniquesenable a real-time oscilloscope to measure signals with similaraccurately as a VNA, within a given a range of frequencies.

In one embodiment, the improved group-delay based averaging techniquesmay be performed by an exemplary general-purpose device 600 such as areal-time oscilloscope—as depicted in FIG. 6. Device 600 may acquiredata signals through a physical input 605 which may be a digital oranalog input, or an interface such as a network, memory, or deviceinterface. In embodiments where interface 605 receives analog signals,analog-to-digital (A/D) converter 610 may be used to convert the analogsignal into a digital signal. In another embodiment, the data signal maybe acquired from memory (for example, memory 620), or from anotherdevice. Memory 620 may store instructions that cause processor 615 toperform the improved group-delay based averaging techniques whenexecuted. Memory 620 may also store data acquired from physicalinterface 605. The one or more intermediate or final results obtainedduring the disclosed methods may be stored in memory 620, output to adifferent device, or used for further operations by processor 615.Memory 620 may comprise one or more separate memories, including memorylocated in one or more other devices.

Although specific embodiments of the invention have been described forpurposes of illustration, it will be apparent to those skilled in theart that various modifications may be made without departing from thespirit and scope of the invention. For example, the disclosed techniquesare not limited to computing s-parameters in real-time oscilloscopes butmay be used to compensate time shifts in any other instruments ordevices, or for other types of signal processing. And, as previouslydiscussed, any suitable methods may be used to determine and compensatefor the group delays. Furthermore, any suitable method of determining orestimating derivatives may be used. For example, as is known in the art,a signal's derivative may be estimated by taking its difference.Although the term “data signal” has been used, it is understood that thepresent techniques may be performed on any type of acquired signal(i.e., “signal under test”). Likewise, one of ordinary skill in the artwill understand the relationship between phase, delay, and group delayof a signal. Accordingly, the invention should not be limited except asby the appended claims.

What is claimed is:
 1. A method for measuring two or more signals undertest, comprising: acquiring two or more signals under test; determiningan average signal based on the two or more signals under test;determining an average group delay for the average signal; determiningindividual group delays for the two or more signals under test;determining differences between the average group delay and theindividual group delays; creating compensated signals by compensatingthe differences; averaging the compensated signals to produce anaveraged result; and outputting the averaged result.
 2. The method ofclaim 1, wherein: the step of determining an average group delaycomprises determining a phase for the average signal; the step ofdetermining individual group delays for the two or more signals undertest comprises determining individual phases for the two or more signalsunder test; and the step of determining differences between the averagegroup delay and the individual group delays comprises determiningdifferences between the average signal phase and the individual phases.3. The method of claim 2, wherein the step of determining a phase of theaverage signal comprises: performing a time-to-frequency transform onthe average signal; and obtaining a phase from the result of thetime-to-frequency transform; and wherein the step of determining phasesof the two or more data signals comprises performing time-to-frequencytransforms on the two or more data signals, and obtaining phases fromthe results of the time-to-frequency transforms.
 4. The method of claim2, wherein the step of determining a phase for the average signalcomprises: calculating a derivative of the average signal; performing atime-to-frequency transform on the derivative of the average signal; andobtaining a phase from the result of the time-to-frequency transform;and wherein the step of determining phases of the two or more datasignals comprises: calculating derivatives of the two or more datasignals; performing time-to-frequency transforms on the derivatives; andobtaining phases from the results of the time-to-frequency transforms.5. The method of claim 2, wherein the step of determining phasedifferences comprises: unwrapping the phase of the average signal;unwrapping the phases of the signals under test; and determining thephase differences by subtracting the unwrapped phase of the averagesignal from the unwrapped phases of the signals under test.
 6. Themethod of claim 2, wherein the differences comprise first differencesand the step of compensating the differences comprises: performing astraight-line fit for each of the differences by using a least meansquared method; obtaining second differences based at least in part onthe slopes; and compensating the second differences.
 7. The method ofclaim 3, wherein the step of compensating the differences furthercomprises: determining time shifts for the two or more signals undertest based on the second differences; and multiplying the results of thetime-to-frequency transforms of the two or more signals under test byexp(j*2π*f*Δt_(i)), where j represents the square root of negative 1, frepresents frequency, and At represents the time shifts.
 8. The methodof claim 3, wherein the step of performing a time-to-frequency transformon the average signal comprises determining a derivative of the averagesignal and performing a time-to-frequency transform on the derivative ofthe average signal; and wherein the step of performing time-to-frequencytransforms on the two or more signals under test comprises determiningderivatives of each of the two or more signals under test and performingtime-to-frequency transforms on the derivatives.
 9. The method of claim4, wherein the step of outputting the averaged result further comprisesintegrating the averaged result.
 10. The method of claim 2, wherein thestep of averaging the compensated signals to produce an averaged resultcomprises; averaging the two or more compensated signals in thefrequency domain to produce an averaged frequency-domain result; andproducing an averaged result by performing a frequency-to-time transformon the averaged frequency-domain result.
 11. The method of claim 2,wherein the step of averaging the compensated signals to produce anaveraged result comprises; creating time-domain compensated signals byperforming a frequency-to-time transform on each compensated signal; andaveraging the time-domain compensated signals to produce an averagedresult.
 12. A measurement instrument configured to compute a group-delaybased averaged result of two or more signals under test, comprising: aphysical interface configured to obtain the two or more signals undertest; memory configured to store digital representations of the two ormore signals under test, and the averaged result; a processor,configured to execute instructions stored in memory; and memoryconfigured to store instructions that, when executed by the processor,perform one of the methods in claims 1-11.
 13. The measurementinstrument of claim 12, further comprising an analog-to-digitalconverter configured to create digital representations of the two ormore signals under test.
 14. A computer-readable medium containinginstructions that, when executed on a processor, performs one of themethods in claims 1-11.